I have a few qualms about the above printed list, mainly that it contains some american animation, but it's rather complete, though I haven't watched half of them (nor would I want to in some cases ^.^; ).
Jin-Roh (And the entire Oshii set along with it, if you're truly an obsessive fan like me of his works ^.^ )
Ghost in the Shell: SAC/2nd GiG (the first and second season of the GitS series, based loosely-though very well done- on the GitS manga.)
Haibane Renmei (Cute, sweet, short. Even I liked it, and I hate happy things. ^.^ )
Wonderful Days (the Blood Opera in the end has CG to DIE for, no pun intended. ^.^ )
Gunslinger Girl (It's a slow, introspective series, but very moving if you watch past the second ep. I fell in love with it during the opening theme song. ^.^ )
Whispers of the Heart (A non Miyazaki work by Studio Ghibli that I pray Disney never ruins. It's by far Ghibli's best work since Grave of the Fireflies.)
The Little Mermaid (an old classic made by Toho back in the 70's, but a very good rendition on the classic faerie tale. Better than Disney anyway, though that isn't giving Toho enough credit. ^.^ )
Innocence: Ghost in the Shell 2 (Not officially released in teh US YET -Sept 17th- but a BEAUTIFUL sequel to the original. Not sure if Dreamworks flopped the subb AGAIN on this one yet, they farked the first subb with Babel Fish >.< )
Serial Experiments Lain (Have YOU seen the Lain? Should be a requirment before you are allowed to touch a computer! >.< )
Battle Royale (Okay, so it isn't an anime, but it really is a great Japanese movie, though you shouldn't watch it around your parents if they don't like violence.)
And yes, Kite (non directors or directors, it's a matter of hentai opinion. I prefer edited) should be seen..... but not until you're over the age of 18, and are POSITIVE no one is going to watch over your back.